The attached article is critical of Buddhism. This is fine.
Of course, it's not the most convincing when someone is happy to collect a salary for 9 years in an institution, only to then criticise the institution once out… but maybe there's nonetheless some wisdom in the criticism. Maybe the 9 years were needed to correctly assess the situation. So let's avoid the ad hominem on the accuser, and let's focus on the accusation.

« Distraught, she went to the monks who explained to her that she was having such trouble now because, in a past life, she was a murderous dictator who burned books, and so now, in this life, she is doomed to forever be learning challenged.Not, "Oh, let's look at changing your study habits", but rather, "Oh, well, that's because you have the soul of a book-burning murderer." »

Well, surely, these monks have understood very little about karma! For karma would also explain why the girl meets circumstances in which she can get help (and 'should' get help, if she met awakened people)! And karma is about habits, not some "just world" fanciful retaliation system!
Karma can never be used to blame victims and leave them there without help (gplus.wallez.name/aHsgb6EMP6x, gplus.wallez.name/1v4J66ZXnJw): if a victim comes to you, it's their karma to have access to some help! So refusing to help, and instead merely blaming the victim, reflects on the bad karma of the potential helper (here the monks), the bad habit of blaming others to justify a lack of compassion! It also says the karma of the sufferer asking for help isn't so bad, if it led to an environment where help could be expected (if not actively refused by deluded people, e.g. in a school)!
A school where no help is given to struggling students isn't really a "school", it's just an endorsement of status quo. A 'school' is meant to challenge the status quo; it is meant for people to leave different from how they came in! These monks have very shallow mastery of the teachings!

Once this is clearly said, the article is clearly pointing not at Buddhism but at "anecdotal evidence".
Are there people who have a less than equanimous, less than wise, less than compassionate 'reading' of Buddhism? Sure!
Does this reflect badly on Buddhism? Or on the human nature always seeking cheap certainties and blaming others rather than taking responsibility to help? I believe it exposes the limitations and dissatisfactions of the ordinary mind of the monks full of certainties and clinging to badly-digested dogma… not so much the limitations of Buddhism.
Unless you also blame 'science' for anyone not understanding perfectly quantum mechanics, fluid mechanics, etc???

One reason I find the article worrying is that after so much time spent in the school, the author has apparently taken very little time to study Buddhism by oneself.
When one writes "Buddhism's inheritance from Hinduism", you know there's a serious lack of knowledge about Buddhism… and this then questions any critique of it! It falls into "straw man" fallacies.
And indeed the representation of Buddhism as the quest for non-existence falls for one of the 'extremes' (nihilism) that Buddhism explicitly rejects!
Another straw man is « There is something dreadfully tragic about believing yourself to have somehow failed your calling whenever joy manages to creep into your life. » It doesn't matter if the error is of the author or of one of the 'monks'. Serious study of Buddhism should have informed the author that Buddhism doesn't reject that there are good things in life, that good karma can even lead to pleasurable existence (higher realms, etc!): Buddhism explicitly rejects that such pleasures can be made 'reliable' and 'permanent', but it doesn't deny their existence nor does it judge them negatively!

« The idea of the void-essence of self is one arrived at through meditation, through exercises in reflection dictated by centuries of tradition. That's enough to give us pause right there – it's not really a process of self-discovery if you're told the method, the steps, and the only acceptable conclusion before you've even begun. »
I'm always having fun with similar statements from 'scientism' (gplus.wallez.name/5TdUYdV23SZ). Please explain to me the scientific method? Reproducibility of results! Another team than the first is told what to do to see if they get the same results, or if a change in circumstances (which were unaccounted for) breaks implicit conditions. The "pause right there", if taken naïvely, rejects science… and if not taken naïvely, then it doesn't reject Buddhist self-less-ness either!

« This is already an unpromising start – if you aren't even allowed variation in the number of sub-navel finger widths for hand placement, how can we hope to be allowed to even slightly differ on the supposed object of inner contemplation? »
Well, if you want to study phase transition between liquid and gas, you're also allowed very little variation in the (temperature, pressure) pair of parameters to apply, and it's dependent on the substance you're studying. Trying to study boiling water below boiling temperature (tied to the pressure at hand) will not get you far either!

« As it turns out, you have as much freedom of inquiry as you had freedom in hand placement. »
Yes, because 2+2=4. It's not freedom to state 2+2=5, it's just delusion and clinging to "well, it should be 5, just because I want it." That's not freedom, that's the dictatorship of ignorant impulses.
Freedom is tied to responsibility, and to seeing reality as it is: it's not living in dream world and denying the real (even when the 'real' is purely a mental or psychological phenomenon! There's no point saying to someone who perceives something that they don't! You can enquire whether the perception is representative of something else, like the vision is representative of a distant object, or merely an optical illusion… you can enquire whether the perception is biased, e.g. by anticipations or desires… whether it's useful, constructive, etc… but there's no point saying to the perceiver "no, you don't perceive this"!). Freedom is within the constraints of reality, it's not 'freedom' to pretend that gravity "shouldn't" apply to you, it's just ignorance (including ignorance of what "freedom" means).

« In a curious twist unique to Buddhism, rigidity of method has infected the structure of belief, ossifying potential explanations of existence into dogmatic assertions mechanically arrived at. »
Any 'model' of reality is like that, not just Buddhism. Even science is rigid at times (not all progresses were immediately acknowledged as such, several theories were rejected for many years prior to being accepted…).

Funnily, even when the author tries to sound positive, the lack of education is glaringly obvious: « At the end of the day, it's still true that, in many respects, Buddhism maintains its moral edge over Christianity or Islam handily. That instinct for proselytising unto war which has made both of these religions such distinctly harmful forces in the story of mankind is nowhere present. »
Nowhere? Not in Myanmar either? Not during the 'purges' in Sri Lanka? There are books on all these, it's not hard to educate oneself that Buddhism's history is tainted, just like any belief system. Maybe there's a difference of degree, but it's not even clear whether it's thanks to the religion being naturally more peaceful (after all, the first buddhist precept, not to kill, is also easily found in Christianity…) or it's merely a historical accident.

« But, the drive to infect individuals with an inability to appreciate life except through a filter of regret and shame » is not a 'drive' that represents Buddhism! Maybe it represents the monks the author met, but not Buddhism, which has sūtras about lay life where wise use and enjoyment of wealth (not poverty, wealth) is discussed, which has sūtras where the enjoyment of good karma in higher realms is discussed, etc.
Joys and appreciations aren't rejected in Buddhism, at all! It's the notions that pleasures can be made 'reliable' and 'permanent' which are rejected.

Basically, the article is a mis-informed attack against religion, instead of attacking the misrepresentations and misunderstandings of a few (who are not necessarily "representative").
Nice try, and correct criticism of certain beliefs ("wrong views"), but wrong target: the wrong beliefs of the monks should be criticised as such. These erroneous views should not however be appropriated as representative of some generic 'Buddhism' label, leading to the generic condemnation of a multitude of traditions.